In micromachined systems, such as micro-electromechanical systems (MEMS) sensors, variable capacitors serve as the interface between a sensor, e.g., an accelerometer, gyroscope, pressure sensor, humidity sensor, or other types of micromachined sensors, and the measurement circuitry. Such sensors have a wide variety of applications including industrial, environmental, and/or physiological monitoring. Physiological monitoring has various biomedical applications including monitoring of posture, activity, gait, intravenous pressure, intracranial pressure, heart sounds, and the like.
In an accelerometer, for example, capacitive plates may be formed by fingers on a beam coupled to a proof mass and fixed fingers coupled to an inertial frame. The sets of fingers are interdigitated and act as capacitor plates that are electrically connected to form variable, differential capacitors. A proof mass is suspended over a substrate by a spring. As the proof mass is deflected in a particular direction, the capacitance measured between a beam finger attached to the proof mass and one of the corresponding fixed fingers coupled to the inertial frame changes, indicating acceleration in a particular direction.
Changes in capacitance due to acceleration along an axis are translated to output voltages by a capacitive interface circuit, which functions as sensing circuitry. For an accelerometer, the capacitive interface circuit processes signals from the variable capacitors to produce sensor signals that represent measurement of motion. The accelerometer may sense motion along one axis, two axes, or three axes.
The variable, differential capacitors in the sensor can be generally approximated as parallel-plate capacitors in which the overlapping area of the plates or the spacing between the plates is a function of the displacement of the beam fingers. The output voltage of a typical switched-capacitor capacitance sensing circuit can be calculated using the following equation:
      v    o    =                    Δ        ⁢                                  ⁢        C                    C        I              ⁢          V      S      where vo is the output voltage of the capacitance sensing circuit, CI is a feedback capacitance associated with the sensing circuit, ΔC is the change in capacitance of the variable capacitors, and VS is the supply voltage.
Because of the size restrictions on the sense element in micromachined systems, the capacitance of the variable capacitors and the change in capacitance is very small, e.g., approximately hundreds of femtofarads to 1-100 attofarads. When the feedback capacitance is approximately the same size as the sense capacitance, the output voltage range is approximately 10 μV to 1 mV and includes sampling noise (kT/C noise). In general, kT/C noise refers to thermal noise in the presence of a filtering capacitor. The kT/C noise is caused by the reset switch of the switched capacitor circuit and is sampled onto the sensing node of the circuit. Consequently, the sensor signal at the output of an amplifier may include amplifier offset, flicker noise (1/f) noise, and kT/C noise that undermine sensor accuracy and performance.